Design method of cascaded active disturbance rejection controller for permanent magnet motors for ship propulsion

Abstract

The present invention discloses a design method of a cascaded auto-disturbance rejection controller for a ship propulsion permanent magnet motor, comprising the following steps: 1. deriving a mathematical model of a permanent magnet motor considering load disturbance and parameter perturbation; 2. cascading a linear extended state observer and a nonlinear extended state observer to determine the structure of a three-stage cascaded auto-disturbance rejection speed controller; 3. designing an extended sliding mode observer to estimate the motor load torque and compensate it in the cascaded extended state observer; 4. adopting an integral sliding mode surface and a power reaching law to design a nonlinear error feedback control law. The method of the present invention has simple steps, enhances the dynamic performance and load disturbance resistance of the system, and improves the response speed and robustness of the system.

Description

Technical Field

[0001] The present invention relates to the field of motor control, and more specifically, to a design method for a cascaded anti-disturbance controller of a ship propulsion permanent magnet motor. Background Art

[0002] Permanent magnet synchronous motors have the advantages of high power density, high efficiency, and high power factor, and have been widely used in ship propulsion, new energy vehicles, rail transportation, etc. The vector control system of permanent magnet synchronous motors mainly includes speed loop and current loop control, among which speed loop control directly determines the system operation performance, and generally adopts PI controller.

[0003] Traditional PI controllers are easy to design and do not rely on motor models. However, for permanent magnet synchronous motor control systems with high coupling, time-varying parameters, and susceptibility to external interference, PI control cannot meet the high-performance and reliable operation of the motor.

[0004] As a new type of controller, the active disturbance rejection controller estimates and compensates for the internal and external disturbances of the system in real time, does not rely on the precise mathematical model of the motor, and has active disturbance rejection capability, so that the system can obtain better dynamic performance and robustness, and is suitable for ship propulsion systems with complex operating conditions. However, for low-speed and high-torque ship propulsion operating conditions, the traditional active disturbance rejection controller cannot guarantee the control performance under large load disturbances, and the traditional active disturbance rejection controller needs to be improved to improve the dynamic response and control robustness of the system under complex and changeable marine conditions. Summary of the invention

[0005] The purpose of the present invention is to provide a design method for a cascaded self-disturbance rejection controller for a permanent magnet motor for ship propulsion, aiming at the application background of low speed and high torque in the field of ship propulsion, so as to enhance the system's ability to resist load disturbances and parameter changes and improve the robustness of the system.

[0006] In order to solve the above technical problems, the present invention adopts a design method of a cascaded active disturbance rejection controller for a ship propulsion permanent magnet motor, comprising the following steps:

[0007] Step 1: In the dual closed-loop vector control of the permanent magnet synchronous motor, the motor motion state equation considering the load disturbance and parameter perturbation is set;

[0008] Step 2: The speed loop adopts a three-stage cascaded anti-disturbance controller, and uses a linear extended state observer and a nonlinear extended state observer in cascade to improve the system's estimation accuracy for large load disturbances;

[0009] Step 3: Use the extended sliding mode observer to estimate the load torque of the motor and compensate it into the cascade extended state observer;

[0010] Step 4: adopt the integral sliding surface and introduce the improved sliding mode reaching law, design the nonlinear error feedback control law, and improve the active disturbance rejection controller based on the nonlinear error feedback control law.

[0011] Furthermore, the step 1 is specifically as follows:

[0012] The motion equation of the motor under load disturbance and parameter perturbation is expressed as:

[0013] ;

[0014] Among them, w e Represents the electrical angular velocity of the motor, n p represents the number of motor poles, J represents the moment of inertia of the motor, Represents the permanent magnet flux of the motor, L d , L q Respectively represent the direct-axis and quadrature-axis inductances of the motor, i d 、i q Represent the direct-axis current and quadrature-axis current of the motor respectively, T L represents the load torque of the motor, B is the damping coefficient of the motor, △T e is the torque perturbation when the parameters are perturbed, which can be expressed as:

[0015] ;

[0016] in, , △L d , △Lq represent the changes of permanent magnet flux, direct-axis inductance and quadrature-axis inductance of the motor respectively.

[0017] Furthermore, the three-stage cascaded anti-disturbance controller in step 2 is specifically:

[0018] Considering the load disturbance and parameter perturbation as total disturbance, the linear extended state observer is constructed as:

[0019] ;

[0020] in, is the error value of the linear extended state observer, is the electrical angular position, L1, L2, L3 are the estimated values ​​of electrical angular position, electrical angular velocity and disturbance in the linear extended state observer, respectively. , , are the gain coefficients of the linear extended state observer, i q * is the given value of the quadrature axis current, b0 is the control coefficient, which can be expressed as:

[0021] ;

[0022] The nonlinear extended state observer is further constructed as:

[0023] ;

[0024] in, is the error value between the estimated position and the actual position, N1, N2, N3 are the estimated values ​​of the electrical angular position, electrical angular velocity and disturbance respectively, , , are the gain coefficients of the linear extended state observer, L3 is the estimated value of the disturbance in the linear extended state observer, is the estimated value of the load torque, is the error feedback function, M=1,2,3, its general form It is expressed as:

[0025] ;

[0026] where sgn() is the sign function;

[0027] The nonlinear error feedback control law is designed as:

[0028] ;

[0029] Where e is the velocity tracking error, N2 is the estimated value of the electrical angular velocity in the nonlinear extended state observer, and w e * is a given electrical angular velocity value, f(e) represents the mathematical model of the feedback control law based on the variable power reaching law, i q0 * is the output current of the error feedback control law;

[0030] The given quadrature axis current output by the three-stage cascaded auto-disturbance rejection controller is expressed as:

[0031] ;

[0032] Among them, N3 and L3 are the disturbance estimates of the linear extended state observer and the nonlinear extended state observer, respectively.

[0033] Furthermore, the method of estimating the load torque by using the extended sliding mode observer described in step 3 is specifically as follows:

[0034] The extended sliding mode observer is designed as:

[0035] ;

[0036] in, is the estimated motor angular velocity, is the estimated value of the load torque, n p is the number of motor pole pairs, J is the rotor moment of inertia, B is the damping coefficient, is the permanent magnet flux, i q is the q-axis current, Z is the sliding mode control law, is the derivative of Z, q and l are the sliding mode control coefficients;

[0037] The sliding surface of the extended sliding mode observer is defined as , the sliding mode reaching law is set as:

[0038] ;

[0039] in, and is the control coefficient of the extended sliding mode observer, k is the gain coefficient of the extended sliding mode observer, sgn( ) is the sign function, Defined as:

[0040] ;

[0041] The sliding mode control law of the extended sliding mode observer is defined as:

[0042] .

[0043] Furthermore, the nonlinear error feedback control law in step 4 is specifically:

[0044] The designed integral sliding surface is:

[0045] ;

[0046] Where e is the velocity tracking error, N2 is the estimated value of the electrical angular velocity in the nonlinear extended state observer, and w e * is the given electrical angular velocity value, g is the integral sliding surface coefficient;

[0047] Design variable power reaching law:

[0048] ;

[0049] in, and is the integral sliding mode control coefficient, k1 and k2 are the integral sliding mode gain coefficients, and sigmoid( ) is the S-type function.

[0050] Compared with the prior art, the present invention has the following advantages:

[0051] 1. In the design process of the cascaded automatic disturbance rejection controller for ship propulsion permanent magnet motors, the present invention combines the actual working conditions of low-speed, high-torque and frequent speed changes of ships, and according to the mathematical model of the permanent magnet motor and the mathematical characteristics of the automatic disturbance rejection controller, adopts a cascade of a linear extended state observer and a nonlinear extended state observer to improve the estimation accuracy of the system for load disturbances and parameter perturbations; designs an extended sliding mode observer to estimate the load torque, and cascades the estimated value compensation value into the extended state observer to improve the control performance of the automatic disturbance rejection controller under large load disturbances; adopts an integral sliding mode surface and introduces a variable power reaching law to design a nonlinear error feedback control law to further improve the response speed and disturbance rejection capability of the automatic disturbance rejection controller.

[0052] 2. The present invention uses the Matlab / Simulink simulation environment to conduct a comparative study on the motor vector control system based on the cascaded anti-disturbance control speed controller and the motor vector control system based on the traditional PI controller. The simulation results show that the system based on the cascaded anti-disturbance control speed controller is superior to the PI system in terms of robustness and dynamic performance.

[0053] 3. The method of the present invention has simple steps and greatly enhances the robustness of the system under conditions of large load disturbance and frequent speed changes in ship propulsion. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a structural block diagram of the ship propulsion permanent magnet motor vector control system of the present invention;

[0055] Figure 2 It is a structural block diagram of a three-stage cascaded auto-disturbance rejection controller in the present invention;

[0056] Figure 3 A comparison diagram of the speed waveforms of the cascaded active disturbance rejection controller system and the PI system when the speed suddenly changes in an embodiment of the present invention;

[0057] Figure 4 This is a comparison diagram of the speed waveforms based on the cascaded anti-disturbance controller system and the PI system when the load is suddenly increased / reduced in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments.

[0059] The design method of the ship propulsion permanent magnet motor cascaded anti-disturbance controller of the present invention comprises the following steps:

[0060] Step 1: In the dual closed-loop vector control of the permanent magnet synchronous motor, derive the motor motion state equation considering load disturbance and parameter perturbation;

[0061] Step 2: The speed loop adopts a three-stage cascaded anti-disturbance controller, and uses a linear extended state observer and a nonlinear extended state observer in cascade to improve the system's estimation accuracy for large load disturbances;

[0062] Step 3: Use the extended sliding mode observer to estimate the motor load torque and compensate it into the cascade extended state observer;

[0063] Step 4: Use the integral sliding surface and introduce the improved sliding mode reaching law to design the nonlinear error feedback control law to further improve the response speed and anti-disturbance capability of the ADRC.

[0064] In this embodiment, the motor motion state equation considering load disturbance and parameter perturbation in step 1 is:

[0065] ;

[0066] where w e Represents the electrical angular velocity of the motor, n p represents the number of motor poles, J represents the moment of inertia of the motor, Represents the permanent magnet flux of the motor, L d , L q represents the direct-axis and quadrature-axis inductance of the motor, i d 、i q Represents the direct-axis current and quadrature-axis current of the motor, T L represents the load torque of the motor, B represents the damping coefficient of the motor, △T e is the torque perturbation when the parameters are perturbed, which can be expressed as:

[0067] ;

[0068] in , △L d , △Lq represents the change in the motor's permanent magnet flux, direct-axis inductance and quadrature-axis inductance.

[0069] In this embodiment, the process of designing the three-stage cascaded anti-disturbance control system in step 2 is as follows:

[0070] Considering the load disturbance and parameter perturbation as total disturbance, the linear extended state observer is constructed as:

[0071] ;

[0072] in, is the error value of the linear extended state observer, is the electrical angular position, L1, L2, L3 are the estimated values ​​of electrical angular position, electrical angular velocity and disturbance in the linear extended state observer, respectively. , , are the gain coefficients of the linear extended state observer, i q * is the given value of the quadrature axis current, b0 is the control coefficient, which can be expressed as:

[0073] ;

[0074] The nonlinear extended state observer is further constructed as:

[0075] ;

[0076] in, is the error value between the estimated position and the actual position, N1, N2, N3 are the estimated values ​​of the electrical angular position, electrical angular velocity and disturbance respectively, , , are the gain coefficients of the linear extended state observer, L3 is the estimated value of the disturbance in the linear extended state observer, is the estimated value of the load torque, is the error feedback function, M=1,2,3, its general form is the error feedback function, which can be expressed as:

[0077] ;

[0078] where sgn() is the sign function.

[0079] The nonlinear error feedback control law is designed as:

[0080] ;

[0081] Where e is the velocity tracking error, N2 is the estimated value of the electrical angular velocity in the nonlinear extended state observer, and w e * is a given electrical angular velocity value, f(e) represents the mathematical model of the feedback control law based on the variable power reaching law, i q0 * is the output current of the error feedback control law.

[0082] The given quadrature axis current output by the three-stage cascaded auto-disturbance rejection controller is expressed as:

[0083] ;

[0084] Among them, N3 and L3 are the disturbance estimates of the linear extended state observer and the nonlinear extended state observer, respectively.

[0085] In this embodiment, the process of designing the extended sliding mode observer to estimate the load torque in step 3 is:

[0086] The extended sliding mode observer is designed as

[0087] ;

[0088] in is the estimated motor angular velocity, is the estimated value of the load torque, n p is the number of motor pole pairs, J is the rotor moment of inertia, B is the damping coefficient, is the permanent magnet flux, i q is the q-axis current, Z is the sliding mode control law, is the derivative of Z, q and l are the sliding mode control coefficients.

[0089] The sliding surface of the observer is defined as , the sliding mode reaching law is set as:

[0090] ;

[0091] in, and is the control coefficient of the extended sliding mode observer, >1,0< <1, k is the gain coefficient of the extended sliding mode observer, sgn( ) is the sign function, Defined as:

[0092] ;

[0093] The sliding mode control law of the extended sliding mode observer is defined as:

[0094] .

[0095] In this embodiment, the process of designing the nonlinear error feedback control law in step 4 is:

[0096] The designed integral sliding surface is:

[0097] ;

[0098] Where e is the velocity tracking error, N2 is the estimated value of the electrical angular velocity in the nonlinear extended state observer, and w e * is the given electrical angular velocity value, g is the integral sliding surface coefficient;

[0099] Design variable power reaching law:

[0100] ;

[0101] in, and is the integral sliding mode control coefficient, >1,0< <1, k1 and k2 are integral sliding mode gain coefficients, and sigmoid( ) is the S-type function.

[0102] The output of the nonlinear error feedback control law is:

[0103] .

[0104] In order to verify the performance of the permanent magnet motor vector control system using cascaded anti-disturbance speed control, a system simulation model was built in Matlab / Simulink and simulation analysis was performed. The rated parameters of the permanent magnet motor in the simulation are: rated speed of 300rpm, AC and DC axis inductance of 10.6315mH, stator resistance of 0.3109Ω, and permanent magnet flux linkage of 1.419Wb.

[0105] In order to verify the superior performance of the cascaded active disturbance rejection controller, the system performance based on the PI controller and the cascaded active disturbance rejection controller was compared and analyzed under the conditions of sudden speed change and sudden load change. Figure 3 The speed waveform comparison diagram of the cascaded anti-disturbance controller system and the PI system when the speed suddenly changes. In the simulation, the operating conditions of the two systems are set as follows: the speed is 100 rpm and no-load operation, suddenly changes to 200 rpm at t=0.3 s, and suddenly changes to 300 rpm at t=0.6 s. Figure 3 It can be seen from the speed response waveform that when the given speed is 100, 200 and 300 rpm, the speed adjustment time is 0.03 s, while the adjustment time of the active disturbance rejection control system is less than 0.01 s. At the same time, the steady-state speed error of the PI system is also greater than that of the active disturbance rejection control system.

[0106] Figure 4 The speed waveform comparison diagram of the cascaded ADRC system and the PI system when the load is suddenly increased or decreased. In the simulation, the operating conditions of the two systems are set as follows: no-load operation with a given speed of 300 rpm, a sudden increase of 1000 Nm at t=0.4 s, and a sudden decrease of 500 Nm at t=0.8 s. Figure 4 The speed response waveform shows that after a sudden load increase, the speed of the PI system will drop and cannot be restored to 300 rpm for stable operation, with a steady-state speed error of about 25 rpm; and after a sudden load reduction, the speed of the PI system will increase, with a steady-state speed error of about 13 rpm. The speed of the ADRC system will drop / increase slightly after a sudden load increase / reduction, but will soon return to stable operation at 300 rpm.

[0107] Therefore, compared with the PI system and the ADRC system, the system based on the cascade ADRC speed controller can quickly achieve no overshoot and has higher robustness to large load disturbances.

[0108] In summary, based on the principle of the active disturbance rejection controller, the present invention designs a third-order active disturbance rejection speed controller based on the cascade extended state observer, and uses it to construct a vector control system for a ship propulsion permanent magnet motor. The system performance based on the PI controller and the active disturbance rejection controller is compared through simulation. The simulation results show that the active disturbance rejection controller enhances the dynamic performance and load disturbance resistance of the system, and improves the response speed and robustness of the system.

[0109] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural change made to the above embodiment based on the technology of the present invention are still within the protection scope of the technical solution of the present invention.

Claims

1. A design method for a cascaded active disturbance rejection controller for a ship propulsion permanent magnet motor, characterized in that: The following steps are involved: Step 1: In the dual closed-loop vector control of the permanent magnet synchronous motor, the motor motion state equation considering the load disturbance and parameter perturbation is set; Step 2: The speed loop adopts a three-stage cascaded auto-disturbance rejection controller, and a linear extended state observer and a nonlinear extended state observer are cascaded to improve the estimation accuracy of the system for large load disturbances; the three-stage cascaded auto-disturbance rejection controller in step 2 is specifically: Considering the load disturbance and parameter perturbation as total disturbance, the linear extended state observer is constructed as: ； in, is the error value of the linear extended state observer, is the electrical angular position, L1, L2, L3 are the estimated values ​​of electrical angular position, electrical angular velocity and disturbance in the linear extended state observer, respectively. , , are the gain coefficients of the linear extended state observer, i q * is the given value of the quadrature axis current, b0 is the control coefficient, which can be expressed as: ； The nonlinear extended state observer is further constructed as: ； in, is the error value of the nonlinear extended state observer, N1, N2, N3 are the estimated values ​​of the electrical angular position, electrical angular velocity and disturbance in the nonlinear extended state observer, respectively. , , are the gain coefficients of the linear extended state observer, L3 is the estimated value of the disturbance in the linear extended state observer, is the estimated value of the load torque, is the error feedback function, M=1,2,3, its general form It is expressed as: ； where sgn() is the sign function; The nonlinear error feedback control law is designed as: ； Where e is the velocity tracking error, N2 is the estimated value of the electrical angular velocity in the nonlinear extended state observer, and w e * is a given electrical angular velocity value, f(e) represents the mathematical model of the feedback control law based on the variable power reaching law, i q0 * is the output current of the error feedback control law; The given quadrature axis current output by the three-stage cascaded auto-disturbance rejection controller is expressed as: ； Among them, N3 and L3 are the disturbance estimates of the linear extended state observer and the nonlinear extended state observer respectively; Step 3: Use an extended sliding mode observer to estimate the load torque of the motor and compensate it in the cascade extended state observer; the method of estimating the load torque using an extended sliding mode observer in step 3 is specifically as follows: The extended sliding mode observer is designed as: ； in, is the estimated motor angular velocity, is the estimated value of the load torque, n p is the number of motor pole pairs, J is the rotor moment of inertia, B is the damping coefficient, is the permanent magnet flux, i q is the q-axis current, Z is the sliding mode control law, is the derivative of Z, q and l are the sliding mode control coefficients; The sliding surface of the extended sliding mode observer is defined as , the sliding mode reaching law is set as: ； in, and is the control coefficient of the extended sliding mode observer, k is the gain coefficient of the extended sliding mode observer, sgn( ) is the sign function, Defined as: ； The sliding mode control law of the extended sliding mode observer is defined as: ； Step 4: adopt the integral sliding surface and introduce the variable power reaching law to design a nonlinear error feedback control law, and improve the active disturbance rejection controller based on the nonlinear error feedback control law.

2. The method for designing a cascaded active disturbance rejection controller for a ship propulsion permanent magnet motor according to claim 1, characterized in that: The step 1 is specifically as follows: The motion equation of the motor under load disturbance and parameter perturbation is expressed as: ； Among them, w e Represents the electrical angular velocity of the motor, n p represents the number of motor poles, J represents the moment of inertia of the motor, Represents the permanent magnet flux of the motor, L d , L q Respectively represent the direct-axis and quadrature-axis inductances of the motor, i d 、i q Represent the direct-axis current and quadrature-axis current of the motor respectively, T L represents the load torque of the motor, B is the damping coefficient of the motor, △T e is the torque perturbation when the parameters are perturbed, which can be expressed as: ； in, , △L d , △L q They respectively represent the changes in the motor's permanent magnet flux, direct-axis inductance and quadrature-axis inductance.

3. The method for designing a cascaded active disturbance rejection controller for a ship propulsion permanent magnet motor according to claim 1, characterized in that: The nonlinear error feedback control law in step 4 is specifically: The designed integral sliding surface is: ； Where e is the velocity tracking error, N2 is the estimated value of the electrical angular velocity in the nonlinear extended state observer, and w e * is the given electrical angular velocity value, g is the integral sliding surface coefficient; Design variable power reaching law: ； in, and is the integral sliding mode control coefficient, k1 and k2 are the integral sliding mode gain coefficients, and sigmoid( ) is the S-type function.

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